Pull up all you can, mow or weed whack the rest and Round-up any new growth. Ivy has thick coated leaves, and Round-up works best on the tender new growth. There are ivy killers out there also, I haven't tried them.

Water the area before you use the herbicide, allow the leaves to dry. This will get it growing, and it will absorb the herbicide better. Also, most herbicids don't work in temps over 85 or so, or they take longer to work. Plants don't metabolize much at higher temps.

I'm sure you know to apply any herbicide on a calm day to avoid it drifting onto plants that you want to keep.

You should check these folks out. They have a page on control methods that is very good.

Scott

Here is a link that might be useful: No ivy

If you don't want to use herbicides on an area you will be using for food, smothering would probably work well in the short term. You could put some organism-rich compost right over it, then spread newspaper over it, then all of your fall leaves, and then soil on top; if you make it about a foot thick it would probably decompose.

How long do you plan to use the area as a vegetable garden? Is there a chance you might want it to revert to ivy at some point?

Creatrix, Scott H, and Eibren,
Thanks for the tips and good advice. Gives me a plan to work this through the Fall and have it ready for Spring. Appears to be less daunting than I initially thought.

I'll be using this new area for vegetables permanently, and have no intent to revert to ivy as a ground cover, as best I can predict.

:) a flame weeder will give you a good head start on killing it- though that black solar oven method that Rizz describes is the perfect backup method (some people shouldn't play with fire. my father is one of them)

you don't have to burn the plants up, just cook them so they wilt. the residual chemicals are minor (it's not like you're spreading lighter fluid on the ground)

lee valley hardware sells both the small kind (takes a little propane tank) and the big one that runs off a big old BBQ tank.

How about the ivy that has crept under the foundation and now under the house???